Recent advances in thin film technology have made it increasingly important to accurately measure the characteristics of thin films. The thin film properties of interest include:
Thickness, d PA0 Index of Refraction, n PA0 Extinction Coefficient, k PA0 Energy Bandgap, E.sub.g PA0 Interface Roughness, .sigma.
The index of refraction n and the extinction coefficient k depend on the energy E of the photons involved; i.e., n=n(E) and k=k (E). The index of refraction n(E) describes how light is diffracted by a material. In similar materials, n(E) scales with the density of the material. The extinction coefficient, k(E), relates to the absorption of light. A material with a large extinction coefficient absorbs more light than a material with a small extinction coefficient. Transparent materials have an extinction coefficient of zero in the visible range of light. The energy bandgap, E.sub.g, represents the minimum photon energy needed for a direct electronic transition from the valence to the conduction band; i.e., for E&lt;E.sub.g, absorption of light due to direct electronic transitions is zero.
In general, the determination of the above quantities is a non-trivial problem. The n(E) and k (E) spectra of a film cannot be measured directly, but must be deduced from optical measurements. U.S. Pat. No. 4,905,170 by Forouhi and Bloomer discloses a method for determining these spectra from the reflectance spectrum of the film. Their method involves shining light onto the film and observing how much light is reflected back. The reflectance spectrum, R(E), is defined as the ratio of the reflected intensity to the incident intensity of light. R(E) depends on the angle of incidence .theta. of the light upon the film, as well as the film thickness d, the indices of refraction and extinction coefficients n.sub.f (E) and k.sub.f (E) of the film, n.sub.s (E) and k.sub.s (E) of the substrate, the band gap energy of the film E.sub.g, and the interface roughness .sigma..sub.1 and .sigma..sub.2 of both the top and the bottom of the film. To characterize any film, it is necessary to de-convolute the optical measurement R(E) into its intrinsic components d, n.sub.f (E), k.sub.f (E), In.sub.s (E), k.sub.s (E),E.sub.g, .sigma..sub.1 and .sigma..sub.2.
The above patent by Forouhi and Bloomer incorporates a formulation for the optical constants n(E) and k(E), along with a parameterized model for interface roughness, into the Fresnel coefficients associated with films on a substrate to generate an algorithm that describes the theoretical reflectance; i.e., EQU R.sub.theory =R.sub.theory (E, .theta., d, n.sub.f (E), k.sub.f (E), n.sub.s (E), k.sub.s (E) E.sub.g, .sigma..sub.1, .sigma..sub.2)
By comparing the resultant equation for theoretical reflectance with the actual measurement of broad-band reflectance, the required parameters for thin film characterization d, n.sub.f (E), k.sub.f (E), E.sub.g, and .sigma..sub.1 and .sigma..sub.2 can be determined.
To measure the reflectance R(E), light must be generated by a source and reflected by the sample into a spectrophotometer. Typically, lenses are used to build optical relays that direct the light from the source to the sample, and from the sample to the spectrophotometer. (An optical relay is a device that produces an image at one point from a source at another point.) The many different materials used in the fabrication of coatings have characteristic reflectance peaks that range from the ultraviolet to the infrared. Therefore, the reflectance spectrum of the sample should be measured for wavelengths in the range from about 190 nm to 1100 nm. Unfortunately, over this wide range of wavelengths, simple lenses exhibit a significant amount of chromatic aberration: the focal length typically changes by about 20% from one end of the spectrum to the other. Therefore any optical relay using lenses will be more efficient at some wavelengths than at others. This means that the measured spectrum will be distorted.
U.S. Pat. No. 4,784,487 by Hopkins and Willis describes an optical relay for spectrophotometric measurements that partially compensates for this chromatic aberration by a skillful use of apertures. There are two difficulties with this relay in the present context. First, the relay was developed for transmittance rather than reflectance measurements. Even if the relay is adapted for reflectance measurements, however, it will still be extremely sensitive to small misalignments. This is because when the light beam reflected by the sample is focused onto the entrance slit of the spectrophotometer, the pencil of light entering the spectrophotometer is not chromatically homogeneous, but is, for example, red in the center and blue toward the edges. If a misalignment occurs, the input beam is no longer exactly centered on the entrance slit, and not only does the intensity of measured light decrease, but the relative ratio of blue to red changes. This is disastrous to the above method of characterizing thin films, since the method relies on measuring all parts of the reflected spectrum equally well. Small and unavoidable misalignments therefore lead to incorrect characterizations of the thin film.
FIG. 1 shows a prior art apparatus for determining the reflectance R(E) of a material. The apparatus is described in U.S. Pat. No. 5,045,704 by Coates and in literature available from Nanometrics Incorporated of Sunnyvale, Calif. This apparatus does not suffer from chromatic aberrations because it uses mirrors rather than lenses to direct light from the source to the sample and from the sample to a spectrophotometer. However, the apparatus has a number of weaknesses. The apparatus uses a beam splitter, so the intensity of the light entering the spectrophotometer is roughly one fourth of the intensity that could be attained by an apparatus with no beam splitter. Furthermore, it is difficult to obtain a beam splitter that works efficiently throughout the wavelength range required.
In the apparatus of FIG. 1, viewing optics are included so that one may visually examine the area of the thin film being measured. However, the image viewed is an image projected upon the surface surrounding the entrance aperture of the spectrophotometer. The image is on the order of 500 microns in diameter, and on this scale most surfaces are noticeably rough. Therefore the image has a grainy appearance.
Furthermore, when using the apparatus of FIG. 1, it is difficult to vary the angles of reflection of light from the sample that are received by the spectrophotometer. At an angle of reflection near 0.degree., the equations for the reflectance R are simpler than at larger angles, and the calculations of optical properties are therefore easier. If the reflectance R is measured at several different angles, however, more information is gained for analysis. It is therefore desirable to use an optical relay that allows for a range of angles of reflection, this range being adjusted to optimize the information obtained for the thin film analysis.
In an apparatus used to characterize a material using reflectance spectrophotometry, it is desirable that light reflected from the material is directed into a spectrophotometer by an optical relay that has a minimum of aberrations. First, as discussed above, it is crucial to eliminate the chromatic aberrations to achieve an accurate measurement. However, lenses and mirrors have other, nonchromatic aberrations as well. These aberrations include spherical aberration, coma, astigmatism, curvature of field, and distortion. All lenses and mirrors suffer from these aberrations to some extent, even if they are perfectly machined. The existence of these aberrations represents a fundamental limitation on the nature of a lens or mirror--a limitation that is generally neglected in the paraxial approximation of introductory texts. Since the thin films of interest often include patterns, such as integrated circuits, it is desirable that a reflectance spectrophotometric apparatus be able to image a small area, on the order of 50 microns in diameter, of the thin film to a spectrophotometer with as little aberration as possible. It is also desirable that the apparatus include hardware for translating the film with respect to the imaging optics so that different regions of the film may be characterized.